2.3.257 Problems 25601 to 25700

Table 2.1057: Main lookup table. Sorted by time used to solve.

#

ID

ODE

Solved?

Maple

Mma

Sympy

time(sec)

25601

1720

\begin{align*} 12 x^{3} y+24 y^{2} x^{2}+\left (9 x^{4}+32 x^{3} y+4 y\right ) y^{\prime }&=0 \\ \end{align*}

78.931

25602

12940

\begin{align*} y y^{\prime \prime }+a {y^{\prime }}^{2}+b y^{2} y^{\prime }+c y^{4}&=0 \\ \end{align*}

78.965

25603

19215

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y^{2}&=0 \\ y \left (0\right ) &= 1 \\ y^{\prime }\left (0\right ) &= 0 \\ \end{align*}

79.006

25604

5165

\begin{align*} x \left (x -2 y\right ) y^{\prime }+y^{2}&=0 \\ \end{align*}

79.026

25605

11909

\begin{align*} y^{\prime }&=\frac {x}{y+\sqrt {x^{2}+1}} \\ \end{align*}

79.043

25606

12930

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}-\left (a y-1\right ) y^{\prime }+2 y^{2} a^{2}-2 b^{2} y^{3}+a y&=0 \\ \end{align*}

79.589

25607

10073

\begin{align*} y^{\prime \prime }&=\frac {1}{y}-\frac {x y^{\prime }}{y^{2}} \\ \end{align*}

79.609

25608

20619

\begin{align*} 4 x^{2} y^{\prime \prime }+4 x^{5} y^{\prime }+\left (x^{3}+6 x^{2}+4\right ) y&=0 \\ \end{align*}

79.628

25609

2943

\begin{align*} y+x y^{2}+\left (x -x^{2} y\right ) y^{\prime }&=0 \\ \end{align*}

79.838

25610

6260

\begin{align*} \left (\operatorname {a4} \,x^{4}+\operatorname {a2} \,x^{2}+\operatorname {a0} \right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

80.089

25611

18719

\begin{align*} y^{\prime \prime }+y^{\prime }+y+y^{3}&=0 \\ \end{align*}

80.112

25612

11631

\begin{align*} \left (y \sqrt {x^{2}+y^{2}}+\left (y^{2}-x^{2}\right ) \sin \left (\alpha \right )-2 x y \cos \left (\alpha \right )\right ) y^{\prime }+x \sqrt {x^{2}+y^{2}}+2 x y \sin \left (\alpha \right )+\left (y^{2}-x^{2}\right ) \cos \left (\alpha \right )&=0 \\ \end{align*}

80.169

25613

5191

\begin{align*} x \left (1-2 y x \right ) y^{\prime }+y \left (2 y x +1\right )&=0 \\ \end{align*}

80.197

25614

11795

\begin{align*} 9 y^{4} \left (x^{2}-1\right ) {y^{\prime }}^{2}-6 x y^{5} y^{\prime }-4 x^{2}&=0 \\ \end{align*}

80.287

25615

13580

\begin{align*} y y^{\prime }+\frac {a \left (5 x +1\right ) y}{2 \sqrt {x}}&=a^{2} \left (-x^{2}+1\right ) \\ \end{align*}

80.315

25616

11769

\begin{align*} x y {y^{\prime }}^{2}+\left (x^{22}-y^{2}+a \right ) y^{\prime }-y x&=0 \\ \end{align*}

80.402

25617

19718

\begin{align*} 2 a x +b y+\left (2 c y+b x +e \right ) y^{\prime }&=g \\ \end{align*}

80.457

25618

11992

\begin{align*} y^{\prime }&=\frac {2 a x +2 a +x^{3} \sqrt {-y^{2}+4 a x}}{\left (x +1\right ) y} \\ \end{align*}

80.530

25619

11792

\begin{align*} x^{2} \left (x y^{2}-1\right ) {y^{\prime }}^{2}+2 x^{2} y^{2} \left (-x +y\right ) y^{\prime }-y^{2} \left (x^{2} y-1\right )&=0 \\ \end{align*}

80.594

25620

6593

\begin{align*} \left (1+{y^{\prime }}^{2}+y y^{\prime \prime }\right )^{2}&=\left (1+{y^{\prime }}^{2}\right )^{3} \\ \end{align*}

80.633

25621

22408

\begin{align*} y^{\prime }&=\frac {y \left (y x +1\right )}{x \left (-y x +1\right )} \\ \end{align*}

80.735

25622

12619

\begin{align*} y^{\prime \prime }&=-\frac {\left (2 x^{2}+1\right ) y^{\prime }}{x \left (x^{2}+1\right )}-\frac {\left (-v \left (v +1\right ) x^{2}-n^{2}\right ) y}{x^{2} \left (x^{2}+1\right )} \\ \end{align*}

80.903

25623

20683

\begin{align*} y^{2}+\left (y x +x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

80.921

25624

12504

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }+2 y^{\prime } x -v \left (v +1\right ) y&=0 \\ \end{align*}

80.994

25625

10411

\begin{align*} y {y^{\prime \prime }}^{3}+y^{3} {y^{\prime }}^{5}&=0 \\ \end{align*}

81.307

25626

20511

\begin{align*} x^{2} y^{\prime \prime }-3 y^{\prime } x +5 y&=x^{2} \sin \left (\ln \left (x \right )\right ) \\ \end{align*}

81.369

25627

11478

\begin{align*} 3 x \left (x^{2}-1\right ) y^{\prime }+x y^{2}-\left (x^{2}+1\right ) y-3 x&=0 \\ \end{align*}

81.384

25628

4113

\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ y \left (0\right ) &= 0 \\ \end{align*}

81.407

25629

23223

\begin{align*} x^{2}+y^{2}-2 y y^{\prime } x&=0 \\ y \left (1\right ) &= 1 \\ \end{align*}

81.458

25630

6090

\begin{align*} \left (c^{2} x^{2}+b^{2}\right ) y-y^{\prime } x +\left (a^{2}-x^{2}\right ) y^{\prime \prime }&=0 \\ \end{align*}

81.515

25631

13493

\begin{align*} x^{2} y^{\prime }&=y^{2} x^{4}+x^{2 n} f \left (a \,x^{n}+b \right )-\frac {n^{2}}{4}+\frac {1}{4} \\ \end{align*}

81.559

25632

13364

\begin{align*} x^{2} y^{\prime }&=y^{2} a^{2} x^{2}-y x +b^{2} \ln \left (x \right )^{n} \\ \end{align*}

81.826

25633

13225

\begin{align*} x^{n +1} y^{\prime }&=x^{2 n} a y^{2}+c \,x^{m}+d \\ \end{align*}

81.914

25634

20100

\begin{align*} \left (5+2 x \right )^{2} y^{\prime \prime }-6 \left (5-2 x \right ) y^{\prime }+8 y&=0 \\ \end{align*}

81.977

25635

14551

\begin{align*} 10 x -4 y+12-\left (x +5 y+3\right ) y^{\prime }&=0 \\ \end{align*}

82.032

25636

13587

\begin{align*} y y^{\prime }-\frac {2 a \left (3 x -10\right ) y}{5 x^{4}}&=\frac {a^{2} \left (x -1\right ) \left (8 x -5\right )}{5 x^{7}} \\ \end{align*}

82.311

25637

19909

\begin{align*} 2 a x +b y+g +\left (2 c y+b x +e \right ) y^{\prime }&=0 \\ \end{align*}

82.549

25638

26053

\begin{align*} \left (x +2 y\right ) {y^{\prime }}^{3}+3 \left (x +y\right ) {y^{\prime }}^{2}+2 y y^{\prime } x&=0 \\ \end{align*}

82.906

25639

14555

\begin{align*} \left (x +y+1\right ) y^{\prime }+1+4 x +3 y&=0 \\ y \left (3\right ) &= -4 \\ \end{align*}

83.039

25640

6258

\begin{align*} -\left (k^{2}-p \left (1+p \right ) \left (-x^{2}+1\right )\right ) y-2 x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right )^{2} y^{\prime \prime }&=0 \\ \end{align*}

83.155

25641

13503

\begin{align*} y y^{\prime }-y&=A \left ({\mathrm e}^{\frac {2 x}{A}}-1\right ) \\ \end{align*}

83.378

25642

14267

\begin{align*} x^{\prime }&=\frac {2 x}{3 t}+\frac {2 t}{x} \\ \end{align*}

83.428

25643

5360

\begin{align*} {y^{\prime }}^{2}+a \,x^{2}+b y&=0 \\ \end{align*}

83.464

25644

20450

\begin{align*} \left (-y+y^{\prime } x \right ) \left (x +y y^{\prime }\right )&=h^{2} y^{\prime } \\ \end{align*}

83.643

25645

23958

\begin{align*} x^{2} y+2 y^{3}-\left (2 x^{3}+3 x y^{2}\right ) y^{\prime }&=0 \\ \end{align*}

83.679

25646

6896

\begin{align*} \left (x +\sqrt {y^{2}-y x}\right ) y^{\prime }-y&=0 \\ \end{align*}

83.751

25647

6836

\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ \end{align*}

83.866

25648

17249

\begin{align*} \frac {9 t}{5}+2 y+\left (2 t +2 y\right ) y^{\prime }&=0 \\ \end{align*}

83.889

25649

22932

\begin{align*} x^{\prime }-x+2 y-z&=t^{2} \\ y^{\prime }+3 x-y+4 z&={\mathrm e}^{t} \\ z^{\prime }-2 x+y-z&=0 \\ \end{align*}

83.896

25650

13433

\begin{align*} y^{\prime }&=\lambda \arccos \left (x \right )^{n} \left (y-a \,x^{m}-b \right )^{2}+a m \,x^{m -1} \\ \end{align*}

84.066

25651

19904

\begin{align*} 3 y-7 x +7+\left (7 y-3 x +3\right ) y^{\prime }&=0 \\ \end{align*}

84.092

25652

204

\begin{align*} 9 \sqrt {x}\, y^{{4}/{3}}-12 x^{{1}/{5}} y^{{3}/{2}}+\left (8 x^{{3}/{2}} y^{{1}/{3}}-15 x^{{6}/{5}} \sqrt {y}\right ) y^{\prime }&=0 \\ \end{align*}

84.210

25653

20744

\begin{align*} {y^{\prime }}^{2} y^{2} \cos \left (a \right )^{2}-2 y^{\prime } x y \sin \left (a \right )^{2}+y^{2}-x^{2} \sin \left (a \right )^{2}&=0 \\ \end{align*}

84.229

25654

13505

\begin{align*} y y^{\prime }-y&=\frac {\left (2 m +1\right ) x}{4 m^{2}}+\frac {A}{x}-\frac {A^{2}}{x^{3}} \\ \end{align*}

84.280

25655

5154

\begin{align*} x \left (2 x^{3}+y\right ) y^{\prime }&=6 y^{2} \\ \end{align*}

84.351

25656

11626

\begin{align*} \left (2 x^{{5}/{2}} y^{{3}/{2}}+x^{2} y-x \right ) y^{\prime }-x^{{3}/{2}} y^{{5}/{2}}+x y^{2}-y&=0 \\ \end{align*}

84.365

25657

11549

\begin{align*} \left (x^{2} y-1\right ) y^{\prime }+8 x y^{2}-8&=0 \\ \end{align*}

84.398

25658

5182

\begin{align*} x \left (-y x +1\right ) y^{\prime }+\left (y x +1\right ) y&=0 \\ \end{align*}

84.475

25659

13339

\begin{align*} \left (a \tanh \left (\lambda x \right )+b \right ) y^{\prime }&=y^{2}+c \tanh \left (\mu x \right ) y-d^{2}+c d \tanh \left (\mu x \right ) \\ \end{align*}

84.579

25660

24328

\begin{align*} y+x \left (3 y x -2\right ) y^{\prime }&=0 \\ \end{align*}

84.612

25661

13967

\begin{align*} \frac {y^{2}-2 x^{2}}{-x^{3}+x y^{2}}+\frac {\left (2 y^{2}-x^{2}\right ) y^{\prime }}{y^{3}-x^{2} y}&=0 \\ \end{align*}

84.839

25662

23863

\begin{align*} x \left (\left (x^{2}+y^{2}\right )^{{3}/{2}}+2 y^{2}\right )+y \left (\left (x^{2}+y^{2}\right )^{{3}/{2}}-2 x^{2}\right ) y^{\prime }&=0 \\ \end{align*}

84.863

25663

23215

\begin{align*} y^{\prime }&=\frac {2 x +y-4}{x -y+1} \\ \end{align*}

84.925

25664

5153

\begin{align*} x \left (2 x^{3}+y\right ) y^{\prime }&=\left (2 x^{3}-y\right ) y \\ \end{align*}

85.139

25665

7743

\begin{align*} x^{2} y^{\prime }+y^{2}&=y y^{\prime } x \\ \end{align*}

85.145

25666

22458

\begin{align*} y^{2}+\left (-x^{3}+y x \right ) y^{\prime }&=0 \\ \end{align*}

85.328

25667

12390

\begin{align*} y^{\prime \prime } x -2 \left (x^{2}-a \right ) y^{\prime }+2 n x y&=0 \\ \end{align*}

85.494

25668

7859

\begin{align*} x y^{2}+y+\left (x^{2} y-x \right ) y^{\prime }&=0 \\ \end{align*}

85.549

25669

7542

\begin{align*} x^{2}-3 y^{2}+2 y y^{\prime } x&=0 \\ \end{align*}

85.837

25670

6082

\begin{align*} p \left (2 k +p \right ) y-\left (1+2 k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

85.859

25671

13533

\begin{align*} y y^{\prime }-y&=-\frac {6}{25} x -A \,x^{2} \\ \end{align*}

85.864

25672

8771

\begin{align*} x^{2} \left (x +1\right ) y^{\prime \prime }+x \left (4 x +3\right ) y^{\prime }-y&=x +\frac {1}{x} \\ \end{align*}

85.936

25673

5185

\begin{align*} x \left (3-y x \right ) y^{\prime }&=y \left (y x -1\right ) \\ \end{align*}

85.954

25674

25769

\begin{align*} y^{\prime }&=x^{2}-y^{2} \\ y \left (0\right ) &= 2 \\ \end{align*}

86.093

25675

21853

\begin{align*} a x y-b +\left (c x y-d \right ) x y^{\prime }&=0 \\ \end{align*}

86.265

25676

13968

\begin{align*} \frac {1}{\sqrt {x^{2}+y^{2}}}+\left (\frac {1}{y}-\frac {x}{y \sqrt {x^{2}+y^{2}}}\right ) y^{\prime }&=0 \\ \end{align*}

86.335

25677

13111

\begin{align*} x^{\prime }&=a x+g y+\beta z \\ y^{\prime }&=g x+b y+\alpha z \\ z^{\prime }&=\beta x+\alpha y+c z \\ \end{align*}

86.938

25678

13325

\begin{align*} \left (\sinh \left (\lambda x \right ) a +b \right ) y^{\prime }&=y^{2}+c \sinh \left (\mu x \right ) y-d^{2}+c d \sinh \left (\mu x \right ) \\ \end{align*}

87.025

25679

5090

\begin{align*} \left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y&=0 \\ \end{align*}

87.551

25680

6050

\begin{align*} y \left (\operatorname {a2} +\operatorname {b2} \,x^{k}+\operatorname {c2} \,x^{2 k}+\left (-1+\operatorname {a1} +\operatorname {b1} \,x^{k}\right ) f \left (x \right )+f \left (x \right )^{2}+f^{\prime }\left (x \right )\right )+x \left (\operatorname {a1} +\operatorname {b1} \,x^{k}+2 f \left (x \right )\right ) y^{\prime }+x^{2} y^{\prime \prime }&=0 \\ \end{align*}

87.694

25681

7422

\begin{align*} x x^{\prime }+t^{2} x&=\sin \left (t \right ) \\ \end{align*}

87.843

25682

5515

\begin{align*} x^{2} {y^{\prime }}^{2}+\left (2 x -y\right ) y y^{\prime }+y^{2}&=0 \\ \end{align*}

87.885

25683

11907

\begin{align*} y^{\prime }&=\frac {x^{{5}/{3}}}{y+x^{{4}/{3}}} \\ \end{align*}

87.902

25684

13834

\begin{align*} 2 x \left (x -1\right ) y^{\prime \prime }+\left (2 x -1\right ) y^{\prime }+\left (a x +b \right ) y&=0 \\ \end{align*}

88.241

25685

13866

\begin{align*} 2 \left (a \,x^{3}+b \,x^{2}+c x +d \right ) y^{\prime \prime }+\left (3 a \,x^{2}+2 b x +c \right ) y^{\prime }+\lambda y&=0 \\ \end{align*}

88.276

25686

13398

\begin{align*} y^{\prime } x&=a \tan \left (\lambda x \right )^{m} y^{2}+k y+a \,b^{2} x^{2 k} \tan \left (\lambda x \right )^{m} \\ \end{align*}

88.279

25687

26224

\begin{align*} \left (x +y\right )^{2} y^{\prime }&=a^{2} \\ \end{align*}

88.289

25688

22559

\begin{align*} y^{2}&=\left (x^{2}+2 y x \right ) y^{\prime } \\ \end{align*}

88.298

25689

12636

\begin{align*} y^{\prime \prime }&=-\frac {2 x y^{\prime }}{x^{2}-1}-\frac {\left (-a^{2} \left (x^{2}-1\right )^{2}-n \left (n +1\right ) \left (x^{2}-1\right )-m^{2}\right ) y}{\left (x^{2}-1\right )^{2}} \\ \end{align*}

88.433

25690

13479

\begin{align*} y^{\prime }&=f \left (x \right ) y^{2}-a \tan \left (\lambda x \right )^{2} \left (a f \left (x \right )-\lambda \right )+a \lambda \\ \end{align*}

88.500

25691

6083

\begin{align*} p \left (1+2 k +p \right ) y-2 \left (1+k \right ) x y^{\prime }+\left (-x^{2}+1\right ) y^{\prime \prime }&=0 \\ \end{align*}

88.786

25692

6196

\begin{align*} \operatorname {a2} x y+\left (\operatorname {b1} \,x^{2}+\operatorname {a1} \right ) y^{\prime }+x^{3} y^{\prime \prime }&=0 \\ \end{align*}

88.924

25693

22400

\begin{align*} 2 x \sin \left (\frac {y}{x}\right )+2 x \tan \left (\frac {y}{x}\right )-y \cos \left (\frac {y}{x}\right )-y \sec \left (\frac {y}{x}\right )^{2}+\left (x \cos \left (\frac {y}{x}\right )+x \sec \left (\frac {y}{x}\right )^{2}\right ) y^{\prime }&=0 \\ \end{align*}

89.398

25694

13278

\begin{align*} \left (a \,x^{n}+x^{m} b +c \right ) y^{\prime }&=a \,x^{-2+n} y^{2}+b \,x^{m -1} y+c \\ \end{align*}

89.496

25695

21768

\begin{align*} y&=2 x +y^{\prime }-\frac {{y^{\prime }}^{3}}{3} \\ \end{align*}

89.536

25696

24386

\begin{align*} a_{1} x +k y+c_{1} +\left (k x +b_{2} y+c_{2} \right ) y^{\prime }&=0 \\ \end{align*}

89.697

25697

13412

\begin{align*} \sin \left (2 x \right )^{n +1} y^{\prime }&=a y^{2} \sin \left (x \right )^{2 n}+b \cos \left (x \right )^{2 n} \\ \end{align*}

89.804

25698

20443

\begin{align*} \left (a {y^{\prime }}^{2}-b \right ) x y+\left (b \,x^{2}-a y^{2}+c \right ) y^{\prime }&=0 \\ \end{align*}

90.014

25699

5007

\begin{align*} x^{n} y^{\prime }&=a^{2} x^{2 n -2}+b^{2} y^{2} \\ \end{align*}

90.052

25700

5152

\begin{align*} x \left (x^{3}+y\right ) y^{\prime }&=\left (x^{3}-y\right ) y \\ \end{align*}

90.165